Search results for: Electromagnetic damper

Authors: S. Kopylov, C. Z. Bo

Abstract:

This study is aimed at exploring the possibility of energy recovery through the suppression of vibrations. The article describes design of electromagnetic dynamic damper. The magnetic part of the device performs the function of a tuned mass damper, thereby providing both energy regeneration and damping properties to the protected mass. According to the theory of tuned mass damper, equations of mathematical models were obtained. Then, under given properties of current system, amplitude frequency response was investigated. Therefore, main ideas and methods for further research were defined.

Keywords: Electromagnetic damper, oscillations with two degrees of freedom, regeneration systems, tuned mass damper.

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Authors: Daniel Y. Abebe, Jeonghyun Jang, Jaehyouk Choi

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This study aims to evaluate the effective size, section and structural characteristics of circular hollow steel (CHS) damper. CHS damper is among steel dampers which are used widely for seismic energy dissipation because they are easy to install, maintain and are inexpensive. CHS damper dissipates seismic energy through metallic deformation due to the geometrical elasticity of circular shape and fatigue resistance around connection part. After calculating the effective size, which is found to be height to diameter ratio of √3, nonlinear FE analyses were carried out to evaluate the structural characteristics and effective section (diameter-to-ratio).

Keywords: Circular hollow steel damper, structural characteristics, effective size, effective section, large deformation, FE analysis.

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Authors: S. S. Ghodsi, M. H. Mehrabi, Zainah Ibrahim, Meldi Suhatril

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This research examines the performance of a hybrid passive control device for enhancing the seismic response of steel frame structures. The device design comprises a damper which employs a viscoelastic material to control both shear and axial strain. In the design, energy is dissipated through the shear strain of a two-layer system of viscoelastic pads which are located between steel plates. In addition, viscoelastic blocks have been included on either side of the main shear damper which obtains compressive strains in the viscoelastic blocks. These dampers not only dissipate energy but also increase the stiffness of the steel frame structure, and the degree to which they increase the stiffness may be controlled by the size and shape. In this research, the cyclical behavior of the damper was examined both experimentally and numerically with finite element modeling. Cyclic loading results of the finite element modeling reveal fundamental characteristics of this hybrid viscoelastic damper. The results indicate that incorporating a damper of the design can significantly improve the seismic performance of steel frame structures.

Keywords: Cyclic loading, energy dissipation, hybrid damper, passive control system, viscoelastic damper.

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Authors: Nitish Kumar Vaja, Oumar Barry, Brian DeJong

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Aeolian vibrations are the major cause for the failure of conductor cables. Using a Stockbridge damper reduces these vibrations and increases the life span of the conductor cable. Designing an efficient Stockbridge damper that suits the conductor cable requires a robust mathematical model with minimum assumptions. However it is not easy to analytically model the complex geometry of the messenger. Therefore an equivalent stiffness must be determined so that it can be used in the analytical model. This paper examines the bending stiffness of the cable and discusses the effect of this stiffness on the natural frequencies. The obtained equivalent stiffness compensates for the assumption of modeling the messenger as a rod. The results from the free vibration analysis of the analytical model with the equivalent stiffness is validated using the full scale finite element model of the Stockbridge damper.

Keywords: Equivalent stiffness, finite element model, free vibration response, Stockbridge damper.

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Authors: Yoonsoo Kim

Abstract:

This paper introduces an open-source software package SCILAB [1], an alternative of MATLAB [2], which can be used for robust control design and analysis of a typical mass-spring-damper (MSD) system. Using the previously published ideas in [3,4], this popular mechanical system is considered to provide another example of usefulness of SCILAB for advanced control design.

Keywords: Robust Control, SCILAB, Mass-Spring-Damper(MSD).

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Authors: Behnam Mehrkian, Arash Bahar, Ali Chaibakhsh

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Magneto-rheological (MR) fluid damper is a semiactive control device that has recently received more attention by the vibration control community. But inherent hysteretic and highly nonlinear dynamics of MR fluid damper is one of the challenging aspects to employ its unique characteristics. The combination of artificial neural network (ANN) and fuzzy logic system (FLS) have been used to imitate more precisely the behavior of this device. However, the derivative-based nature of adaptive networks causes some deficiencies. Therefore, in this paper, a novel approach that employ genetic algorithm, as a free-derivative algorithm, to enhance the capability of fuzzy systems, is proposed. The proposed method used to model MR damper. The results will be compared with adaptive neuro-fuzzy inference system (ANFIS) model, which is one of the well-known approaches in soft computing framework, and two best parametric models of MR damper. Data are generated based on benchmark program by applying a number of famous earthquake records.

Keywords: Benchmark program, earthquake record filtering, fuzzy logic, genetic algorithm, MR damper.

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Authors: P. Sowa

Abstract:

The article reviews the current state of large-scale studies about the impact of electromagnetic field on natural environment. The scenario of investigations – simulation of natural conditions at the workplace, taking into consideration the influence both low and high frequency electromagnetic fields is shown.The biological effects of low and high frequency electromagnetic fields are below presented. Results of investigation with animals are shown. The norms and regulations concerning the levels of electromagnetic field intensity are reviewed.

Keywords: Electromagnetic field and environment, biological effects of electric field on human body, simulation of natural condition at workplace

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Authors: Se Kyung Oh, Young Hwan Yoon, Ary Bachtiar Krishna

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Nowadays, a passenger car suspension must has high performance criteria with light weight, low cost, and low energy consumption. Pilot controlled proportional valve is designed and analyzed to get small pressure change rate after blow-off, and to get a fast response of the damper, a reverse damping mechanism is adapted. The reverse continuous variable damper is designed as a HS-SH damper which offers good body control with reduced transferred input force from the tire, compared with any other type of suspension system. The damper structure is designed, so that rebound and compression damping forces can be tuned independently, of which the variable valve is placed externally. The rate of pressure change with respect to the flow rate after blow-off becomes smooth when the fixed orifice size increases, which means that the blow-off slope is controllable using the fixed orifice size. Damping forces are measured with the change of the solenoid current at the different piston velocities to confirm the maximum hysteresis of 20 N, linearity, and variance of damping force. The damping force variance is wide and continuous, and is controlled by the spool opening, of which scheme is usually adapted in proportional valves. The reverse continuous variable damper developed in this study is expected to be utilized in the semi-active suspension systems in passenger cars after its performance and simplicity of the design is confirmed through a real car test.

Keywords: Blow-off, damping force, pilot controlledproportional valve, reverse continuous damper.

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Authors: M. Yoneda

Abstract:

It is known that stationary human occupants act as dynamic mass-spring-damper systems and can change the modal properties of civil engineering structures. This paper describes the full scale measurement to explain the tuned mass damper effects of stationary people on structural damping of footbridge with center span length of 33 m. A human body can be represented by a lumped system consisting of masses, springs, and dashpots. Complex eigenvalue calculation is also conducted by using ISO5982:1981 human model (two degree of freedom system). Based on experimental and analytical results for the footbridge with the stationary people in the standing position, it is demonstrated that stationary people behave as a tuned mass damper and that ISO5982:1981 human model can explain the structural damping characteristics measured in the field.

Keywords: Dynamic interaction, footbridge, stationary people, structural damping.

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Authors: Michael Schukat

Abstract:

Electromagnetic flowmeters with DC excitation are used for a wide range of fluid measurement tasks, but are rarely found in dosing applications with short measurement cycles due to the achievable accuracy. This paper will identify a number of factors that influence the accuracy of this sensor type when used for short-term measurements. Based on these results a new signal-processing algorithm will be described that overcomes the identified problems to some extend. This new method allows principally a higher accuracy of electromagnetic flowmeters with DC excitation than traditional methods.

Keywords: Electromagnetic Flowmeter, Kalman Filter, ShortMeasurement Cycles, Signal Estimation

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Authors: Iliana Marinova, Valentin Mateev

Abstract:

For investigations of electromagnetic field distributions in biological structures by Finite Element Method (FEM), a method for automatic 3D model building of human anatomical objects is developed. Models are made by meshed structures and specific electromagnetic material properties for each tissue type. Mesh is built according to specific FEM criteria for achieving good solution accuracy. Several FEM models of anatomical objects are built. Formulation using magnetic vector potential and scalar electric potential (A-V, A) is used for modeling of electromagnetic fields in human tissue objects. The developed models are suitable for investigations of electromagnetic field distributions in human tissues exposed in external fields during magnetic stimulation, defibrillation, impedance tomography etc.

Keywords: electromagnetic field, finite element method, humantissue.

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Authors: A. Ashfak, A. Saheed, K. K. Abdul Rasheed, J. Abdul Jaleel

Abstract:

This paper presents the design, fabrication and evaluation of magneto-rheological damper. Semi-active control devices have received significant attention in recent years because they offer the adaptability of active control devices without requiring the associated large power sources. Magneto-Rheological (MR) dampers are semi- active control devices that use MR fluids to produce controllable dampers. They potentially offer highly reliable operation and can be viewed as fail-safe in that they become passive dampers if the control hardware malfunction. The advantage of MR dampers over conventional dampers are that they are simple in construction, compromise between high frequency isolation and natural frequency isolation, they offer semi-active control, use very little power, have very quick response, has few moving parts, have a relax tolerances and direct interfacing with electronics. Magneto- Rheological (MR) fluids are Controllable fluids belonging to the class of active materials that have the unique ability to change dynamic yield stress when acted upon by an electric or magnetic field, while maintaining viscosity relatively constant. This property can be utilized in MR damper where the damping force is changed by changing the rheological properties of the fluid magnetically. MR fluids have a dynamic yield stress over Electro-Rheological fluids (ER) and a broader operational temperature range. The objective of this papert was to study the application of an MR damper to vibration control, design the vibration damper using MR fluids, test and evaluate its performance. In this paper the Rheology and the theory behind MR fluids and their use on vibration control were studied. Then a MR vibration damper suitable for vehicle suspension was designed and fabricated using the MR fluid. The MR damper was tested using a dynamic test rig and the results were obtained in the form of force vs velocity and the force vs displacement plots. The results were encouraging and greatly inspire further research on the topic.

Keywords: Magneto-rheological Fluid, MR Damper, Semiactive controller, Electro-rheological fluid.

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Authors: Min Sang Lee, Hee Jae Shin, In Pyo Cha, Hyun Kyung Yoon, Seong Woo Hong, Min Jae Yu, Hong Gun Kim, Lee Ku Kwac

Abstract:

In this paper, the electromagnetic shielding characteristics of an up-to-date typical carbon filler material, carbon fiber used with a metal mesh were investigated. Carbon fiber 12k-prepregs, where carbon fibers were impregnated with epoxy, were laminated with wire meshes, vacuum bag-molded and hardened to manufacture hybrid-type specimens, with which an electromagnetic shield test was performed in accordance with ASTM D4935-10, through which was known as the most excellent reproducibility is obtainable among electromagnetic shield tests. In addition, glass fiber prepregs whose electromagnetic shielding effect were known as insignificant were laminated and formed with wire meshes to verify the validity of the electromagnetic shield effect of wire meshes in order to confirm the electromagnetic shielding effect of metal meshes corresponding existing carbon fiber 12k-prepregs. By grafting carbon fibers, on which studies are being actively underway in the environmental aspects and electromagnetic shielding effect, with hybrid-type wire meshes that were analysed through the tests, in this study, the applicability and possibility are proposed.

Keywords: Carbon Fiber Reinforced Plastic (CFRP), Glass Fiber Reinforced Plastic (GFRP), Stainless Wire Mesh, Electromagnetic Shielding.

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Authors: C. Temaneh-Nyah, J. Makiche, J. Nujoma

Abstract:

This paper considers the characterization of a complex electromagnetic environment due to multiple sources of electromagnetic radiation as a five-dimensional surface which can be described by a set of several surface sections including: instant EM field intensity distribution maps at a given frequency and altitude, instantaneous spectrum at a given location in space and the time evolution of the electromagnetic field spectrum at a given point in space. This characterization if done over time can enable the exposure levels of Radio Frequency Radiation at every point in the analysis area to be determined and results interpreted based on comparison of the determined RFR exposure level with the safe guidelines for general public exposure given by recognized body such as the International commission on non-ionizing radiation protection (ICNIRP), Institute of Electrical and Electronic Engineers (IEEE), the National Radiation Protection Authority (NRPA).

Keywords: Electromagnetic Environment, Electric Field Strength, Mathematical Models.

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Authors: Adnan Muharemovic, Hidajet Salkic, Mario Klaric, Irfan Turkovic, Aida Muharemovic

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In nature, electromagnetic fields always appear like atmosphere static electric field, the earth's static magnetic field and the wide-rang frequency electromagnetic field caused by lightening. However, besides natural electromagnetic fields (EMF), today human beings are mostly exposed to artificial electromagnetic fields due to technology progress and outspread use of electrical devices. To evaluate nuisance of EMF, it is necessary to know field intensity for every frequency which appears and compare it with allowed values. Low frequency EMF-s around transmission and distribution lines are time-varying quasi-static electromagnetic fields which have conservative component of low frequency electrical field caused by charges and eddy component of low frequency magnetic field caused by currents. Displacement current or field delay are negligible, so energy flow in quasi-static EMF involves diffusion, analog like heat transfer. Electrical and magnetic field can be analyzed separately. This paper analysis the numerical calculations in ELF-400 software of EMF in distribution substation in shopping center. Analyzing the results it is possible to specify locations exposed to the fields and give useful suggestion to eliminate electromagnetic effect or reduce it on acceptable level within the non-ionizing radiation norms and norms of protection from EMF.

Keywords: Electromagnetic Field, Density of Electromagnetic Flow, Place of Proffesional Exposure, Place of Increased Sensitivity

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Authors: C. Temaneh Nyah

Abstract:

The analysis of electromagnetic environment using deterministic mathematical models is characterized by the impossibility of analyzing a large number of interacting network stations with a priori unknown parameters, and this is characteristic, for example, of mobile wireless communication networks. One of the tasks of the tools used in designing, planning and optimization of mobile wireless network is to carry out simulation of electromagnetic environment based on mathematical modelling methods, including computer experiment, and to estimate its effect on radio communication devices. This paper proposes the development of a statistical model of electromagnetic environment of a mobile wireless communication network by describing the parameters and factors affecting it including the propagation channel and their statistical models.

Keywords: Electromagnetic Environment, Statistical model, Wireless communication network.

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Authors: Hussam Elias, Ninovic Perez, Holger Hirsch

Abstract:

With ever-increasing use of equipment, device or more generally any electrical or electronic system, the chance of Electromagnetic incompatibility incidents has considerably increased which demands more attention to ensure the possible risks of these technologies. Therefore, complying with certain Electromagnetic compatibility (EMC) rules and not overtaking an acceptable level of radiated emissions are utmost importance for the diffusion of electronic products. In this paper, developed measure tool and a convolutional neural network were used to propose a method to reduce the required time to carry out the final measurement phase of Electromagnetic interference (EMI) measurement according to the norm EN 55032 by predicting the radiated emission and determining the height of the antenna that meets the maximum radiation value.

Keywords: Antenna height, Convolutional Neural Network, Electromagnetic Compatibility, Mean Absolute Error, position error.

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Authors: Ilona I. Iatcheva, Rumena D. Stancheva, Mario Metodiev

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The paper deals with determination of electromagnetic and temperature field distribution of induction heating system used for pipe brazing. The problem is considered as coupled – time harmonic electromagnetic and transient thermal field. It has been solved using finite element method. The detailed maps of electromagnetic and thermal field distribution have been obtained. The good understanding of the processes in the considered system ensures possibilities for control, management and increasing the efficiency of the welding process.

Keywords: Electromagnetic field, temperature field, finiteelement method, induction heating, pipe brazing.

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Authors: Shun-Chang Chang

Abstract:

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.

Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.

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Authors: H.S. Kim

Abstract:

In this study, control performance of a smart base isolation system consisting of a friction pendulum system (FPS) and a magnetorheological (MR) damper has been investigated. A fuzzy logic controller (FLC) is used to modulate the MR damper so as to minimize structural acceleration while maintaining acceptable base displacement levels. To this end, a multi-objective optimization scheme is used to optimize parameters of membership functions and find appropriate fuzzy rules. To demonstrate effectiveness of the proposed multi-objective genetic algorithm for FLC, a numerical study of a smart base isolation system is conducted using several historical earthquakes. It is shown that the proposed method can find optimal fuzzy rules and that the optimized FLC outperforms not only a passive control strategy but also a human-designed FLC and a conventional semi-active control algorithm.

Keywords: Fuzzy logic controller, genetic algorithm, MR damper, smart base isolation system

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Authors: M. Karamifard, M. Kazeminejad, A. Maghsoodloo

Abstract:

Electromagnetic flow meter by measuring the varying of magnetic flux, which is related to the velocity of conductive flow, can measure the rate of fluids very carefully and precisely. Electromagnetic flow meter operation is based on famous Faraday's second Law. In these equipments, the constant magnetostatic field is produced by electromagnet (winding around the tube) outside of pipe and inducting voltage that is due to conductive liquid flow is measured by electrodes located on two end side of the pipe wall. In this research, we consider to 2-dimensional mathematical model that can be solved by numerical finite difference (FD) solution approach to calculate induction potential between electrodes. The fundamental concept to design the electromagnetic flow meter, exciting winding and simulations are come out by using MATLAB and PDE-Tool software. In the last stage, simulations results will be shown for improvement and accuracy of technical provision.

Keywords: Electromagnetic Flow Meter, Induction Voltage, Finite Difference

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Authors: Leila Amjad, Mahsa Shafighi

Abstract:

The role of the pollen grain, with to the reproductive process of higher plants, is to deliver the spermatic cells to the embryo sac for egg fertilization. The aim of this project was study the effect of electromagnetic fields on structure and pollen grains development in Chenopodium album. Anthers of Chenopodium album L. were collected at different stages of development from control (without electromagnetic field) and plants grown at 10m from the field sources. Structure and development of pollen grains were studied and compared. The studying pollen structure by Light and Scanning electron microscopy showed that electromagnetic fields reduction of pollen grains number and male sterility, thus , in some anthers, pollen grains were attached together and deformed compared to control ones. The data presented suggest that prolonged exposures of plants to magnetic field may cause different biological effects at the cellular tissue and organ levels.

Keywords: Electromagnetic fields, pollen, Chenopodium albumL.

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Authors: Apetsi K. Ampiah, Zhao Xin

Abstract:

Earthquakes over the years have been known to cause devastating damage on buildings and induced huge loss on human life and properties. It is for this reason that engineers have devised means of protecting buildings and thus protecting human life. Since the invention of devices such as the viscous and friction dampers, scientists/researchers have been able to incorporate these devices into buildings and other engineering structures. The viscous damper is a hydraulic device which dissipates the seismic forces by pushing fluid through an orifice, producing a damping pressure which creates a force. In the friction damper, the force is mainly resisted by converting the kinetic energy into heat by friction. Devices such as viscous and friction dampers are able to absorb almost all the earthquake energy, allowing the structure to remain undamaged (or with some amount of damage) and ready for immediate reuse (with some repair works). Comparing these two devices presents the engineer with adequate information on the merits and demerits of these devices and in which circumstances their use would be highly favorable. This paper examines the performance of both viscous and friction dampers under different ground motions. A two-storey frame installed with both devices under investigation are modeled in commercial computer software and analyzed under different ground motions. The results of the performance of the structure are then tabulated and compared. Also included in this study is the ease of installation and maintenance of these devices.

Keywords: Friction damper, seismic, slip load, viscous damper.

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Authors: Iliana Marinova, Valentin Mateev

Abstract:

In this paper a computer system for electromagnetic properties measurements is designed. The system employs Agilent 4294A precision impedance analyzer to measure the amplitude and the phase of a signal applied over a tested biological tissue sample. Measured by the developed computer system data could be used for tissue characterization in wide frequency range from 40Hz to 110MHz. The computer system can interface with output devices acquiring flexible testing process.

Keywords: Electromagnetic properties, human tissue, bioimpedance, measurement system.

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Authors: Ahmed Nouainia, Mohamed Hajji, Taoufik Aguili

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In this paper, an electromagnetic analysis is presented for describing the influence of shielding in a rectangular waveguide. A hybridization based on the method of moments combined to the generalized equivalent circuit MoM-GEC is used to model the problem. This is validated by applying the MoM-GEC hybridization to investigate a diffraction structure. It consists of electromagnetic diffraction by an iris in a rectangular waveguide. Numerical results are shown and discussed and a comparison with FEM and Marcuvitz methods is achieved.

Keywords: Inductive irises, MoM-GEC, waveguide, shielding.

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Authors: J. Vaseghi, S.Navaei, B. Navayinia, F. Roshantabari

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In This paper, the behavior of eccentric braced frame (EBF) is studied with replacing friction damper (FD) in confluence of these braces, in 5 and 10-storey steel frames. For FD system, the main step is to determine the slip load. For this reason, the performance indexes include roof displacement, base shear, dissipated energy and relative performance should be investigated. In nonlinear dynamic analysis, the response of structure to three earthquake records has been obtained and the values of roof displacement, base shear and column axial force for FD and EBF frames have been compared. The results demonstrate that use of the FD in frames, in comparison with the EBF, substantially reduces the roof displacement, column axial force and base shear. The obtained results show suitable performance of FD in higher storey structure in comparison with the EBF.

Keywords: Friction Damper (FD), Slip Load, Nonlinear Dynamic Analysis, Performance Index.

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Authors: Krishna Mohana Rao, G. Ravi Kumar, P. Sowmya

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This paper presents a study of the Taguchi design application to optimize surface quality in damper inserted end milling operation. Maintaining good surface quality usually involves additional manufacturing cost or loss of productivity. The Taguchi design is an efficient and effective experimental method in which a response variable can be optimized, given various factors, using fewer resources than a factorial design. This Study included spindle speed, feed rate, and depth of cut as control factors, usage of different tools in the same specification, which introduced tool condition and dimensional variability. An orthogonal array of L9(3^4)was used; ANOVA analyses were carried out to identify the significant factors affecting surface roughness, and the optimal cutting combination was determined by seeking the best surface roughness (response) and signal-to-noise ratio. Finally, confirmation tests verified that the Taguchi design was successful in optimizing milling parameters for surface roughness.

Keywords: ANOVA, Damper, End Milling, Optimization, Surface roughness, Taguchi design.

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Authors: Hussam Elias, Ninovic Perez, Holger Hirsch

Abstract:

The completion of the EMC regulations worldwide is growing steadily as the usage of electronics in our daily lives is increasing more than ever. In this paper, we present a method to perform the final phase of Electromagnetic Compatibility (EMC) measurement and to reduce the required test time according to the norm EN 55032 by using a developed tool and the Conventional Neural Network (CNN). The neural network was trained using real EMC measurements which were performed in the Semi Anechoic Chamber (SAC) by CETECOM GmbH in Essen Germany. To implement our proposed method, we wrote software to perform the radiated electromagnetic interference (EMI) measurements and use the CNN to predict and determine the position of the turntable that meet the maximum radiation value.

Keywords: Conventional neural network, electromagnetic compatibility measurement, mean absolute error, position error.

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Authors: Daniel Y. Abebe, Jaehyouk Choi

Abstract:

There are several types of metal-based devices conceived as dampers for the seismic energy absorber whereby damages to the major structural components could be minimized for both new and existing structures. This paper aimed to develop and evaluate structural performance of slit circular shear panel damper for passive seismic energy protection by inelastic deformation. Structural evaluation was done using commercially available nonlinear FE simulation program. The main parameters considered are: diameter-to-thickness (D/t) ratio and slit length-to-width ratio (l/w). Depending on these parameters three different buckling mode and hysteretic behavior was found: yielding prior to buckling without strength degradation, yielding prior to buckling with strength degradation and yielding with buckling and strength degradation which forms pinching at initial displacement. The susceptible location at which the possible crack is initiated is also identified for selected specimens using rupture index.

Keywords: Slit circular shear panel damper, Hysteresis Characteristics, Slip length-to-width ratio, D/t ratio, FE analysis.

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Authors: Tawiwat V., Narongkorn D., Auttapoom L.

Abstract:

This research proposes the change of damping coefficient regarding minimum displacement. From the mass with external forced and damper problem, when is the constant external forced transmitted to the understructure in the difference angle between 30 and 60 degrees. This force generates the vibration as general known; however, the objective of this problem is to have minimum displacement. As the angle is changed and the goal is the same; therefore, the damper of the system must be varied while keeping constant spring stiffness. The problem is solved by using nonlinear programming and the suitable changing of the damping coefficient is provided.

Keywords: Damping coefficient, Optimal control, Minimum Displacement and Vibration

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